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A Canadian writer says

In the limit, we will be able to create bionic humans. Progress towards this goal was portrayed in a remarkable video...

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    In this case, “in the limit” is just an ingredient in the writer’s word salad. Technically, a limit is something you can approach to any measure of closeness, but never actually have to reach. However, in order to be close to something, you have to define it precisely enough to measure a distance. A “bionic human” is too vague a term to use this way. In fact, if we’re talking about a process where biological parts are replaced with mechanical parts, the limit is not a “bionic human”, but a humanoid robot, in which the biological component has been reduced to zero (a genuine physical limit). – Global Charm Jul 7 at 6:33
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To me, this means

We will keep taking steps towards the creation of bionic humans. It is not known whether we will get all the way there.

Let's look at an example. Here's the graph of f(x) = 1/x:

graph of 1 over x

We say that the limit of f(x) as x approaches infinity is 0. (We can also say that the limit of f(x) as x approaches negative infinity is 0. But this limit is different, because we're traveling through negative values to almost get to 0, whereas in the first case we were traveling through positive values.)

There are other limits where the limit value is actually reached. But this is a case where it never gets reached.

When authors use technical language from another field, applied to something quite different, it might be because the author is just so used to using that technical language, that s/he extends it in an intuitive way without thinking too much about it.

The downside of borrowing a technical term in this way is that the idea the author is trying to convey doesn't always end up super clear.

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This is a term borrowed from differential calculus. That begins with the study of infinitesimals, the tiniest conceivable values and how to manage them. The method is to describe a variable in an equation and plan on what happens as the variable goes to a limit, often infinity. The endpoint of such mental, analytical processes is called "in the limit."

For purposes of the given text they mean that it will happen eventually no matter what.

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    The two parts of this answer seem to be in tension with each other. Ordinarily, when people say that something will happen 'no matter what' they mean that it will happen within some finite time, not that it is 'in the limit' of some infinitely long process. – jsw29 Jul 7 at 3:43

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